For homework, Ari had to find 5% of $900. Did he do the work correctly?

Question

A tape diagram. There are 5 parts out of a whole of 100. There are question mark parts out of a whole of 900.

StartFraction part Over whole EndFraction = StartFraction 100 times 180 Over 5 times 180 EndFraction = StartFraction 18,000 Over 900 EndFraction

Are Ari’s calculations correct?

No. Ari multiplied the denominators incorrectly.
No. Ari should have written the percent ratio as StartFraction 5 Over 100 EndFraction
No. Ari should have divided, not multiplied.
Yes. Ari’s work is correct.

Answer 1

To find 5% of $900, you can use the formula:

\[ \text{Percentage} = \left(\frac{\text{Percent}}{100}\right) \times \text{Whole} \]

In this case:

\[ \text{Percentage} = \left(\frac{5}{100}\right) \times 900 = 0.05 \times 900 = 45 \]

Let's analyze Ari's calculations based on the information given:

1. Ari illustrated the division incorrectly by stating "StartFraction part Over whole EndFraction = StartFraction 100 times 180 Over 5 times 180 EndFraction = StartFraction 18,000 Over 900 EndFraction," which does not directly relate to what he was trying to calculate.
2. The question states there are 5 parts out of 100, which is correct, but Ari's approach to calculating using a tape diagram and manipulating the fractions appears to be incorrect.

Ari's error in calculating seems to stem from incorrect operations and interpretations of the fractions. Therefore, the most accurate choice is:

No. Ari should have written the percent ratio as StartFraction 5 Over 100 EndFraction.

While there are multiple issues with his calculations and approach, this statement captures the error in representation of the percent.